帮看看下图题目的极限是 -1/2吗?答案说是1/2 - 知识问答

帮看看下图题目的极限是 -1/2吗?答案说是1/2,可我算出来是负的

1个回答

lim(x→0) ∫[0,x] (tant-sint)dt/(cosx-1)^2
=lim(x→0) ∫[0,x] (tant-sint)dt/(-x^2/2)^2
=lim(x→0) 4∫[0,x] (tant-sint)dt/x^4
=lim(x→0) 4(tanx-sinx)/(4x^3)
=lim(x→0) tanx(1-cosx)/(x^3)
=lim(x→0) (x^2/2)/(x^2)
=1/2

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